I would say that it is possible to do this kind of thing (and probably the easiest way to do it) with SDL or SMFL and you should probably know OpenGL if you wish to make those kind of effects. More or less this is doable in any 2d api if you put more time in it. Graphics in the clip are done with sprites and sprite animation for the most part, so you can achive this level of quality with any kind of drawing software.

essentially, as you move along, you record several points(position, and direction of thruster, and a time to live for that point).

you generate a series of rectangles starting at the source thruster, and create a rectangle between the current point and the next point(using perpendicular direction from each points's recored rotation).

basically this diagram well hopefully explain it well enough:

to see the above method in action:

their are other ways(such as re-drawing the previous frame, but fading it out a bit, then draw the current frame).